Searching the web, Heres some notes on Ulric
Ulric is portrayed as a massive warrior, armored in the style of the barbarians who inhabited the Empire several centuries ago. He wears a silver gray wolf-skin cloak and wields a massive waraxe named Blitzbeil. He can take the form of a huge silver-gray wolf. Ulric is a distant, harsh, and unforgiving god, who expects his followers to stand on their own two feet and put their faith in martial prowess. He despises weakness, cowardice, and trickery, and expects his followers to always take the direct approach to solving a problem.
Bravery, self-reliance and strength are the greatest virtues. Underhandedness of any kind are dishonorable and at odds with Ulric's nature of directness and honor. Obey your military superiors and never refuse an order unless doing so would break another of Ulric's tenets. Never refuse a direct challenge. Modern weapons, such as gunpowder weapons, artillery, crossbows and fire-bombs, because they do not rely any physical strength are shunned. Followers of Ulric must never allow one of the fires of a shrine or temple to go out. Oppose Chaos wherever you see it. Never flee a fight unless facing overwhelming odds and the greater good would be served by such a flight.
The problem is your thinking of Ulric worship like a wolf with a wolves mindset. What you should think of is him as a Honorable Barbarian who relies on strength to deal with a problem. Funny, I always pictured them like a bear rather than a wolf.
Do wolves sneak up on you? I thought they howled and thus gave advance warning? I know they are fast, cunning and fierce.
This is the my view on a Ulric follower on the way I read how a follower of Ulric acts. = I always pictured them like a bear rather than a wolf.
I also think that a god wouldnt let you access his spells if your of another faith. But back in 1st edition, and maybe in 2nd. There were general Cleric spells anyone could access, as well as worshipper only spells. So you had more choice.
But how could you have a chaos worshiping sigmaritte if all you had to do was ask him to cast a sigmar spell and if he couldnt he was a heretic? Be too easy.
If you look at the Chaos gods their worshippers get access to Dark magic + their chosen chaos gods magic, from the books I read etc.
Maybe have those other gods spells work to a lesser extent than a true follower? I dont know as, I didnt forsee an issue, never played a Priest/Cleric.